论文标题
$ \ mathbb {q}/\ mathbb {z} $对称
$\mathbb{Q}/\mathbb{Z}$ symmetry
论文作者
论文摘要
我们用离散对称性$ \ MATHBB {Q}/\ MATHBB {Z} $总结量子字段理论的基本特征（可能更高的形式，全局或测量）。表示和异常的分类相当丰富，涉及整数的环。作为一个主要示例，我们详细考虑了3D拓扑dijkgraaf-witten $ \ mathbb {q}/\ mathbb {z} $ gauge理论。我们还简要讨论了一些先前考虑的物理系统的相关性。特别是，我们评论了与最近发现的4D QED中不可脱落的对称性的关系以及Chern-Simons TQFT的分类问题。
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of profinite integers. As a main example we consider in detail 3d topological Dijkgraaf-Witten $\mathbb{Q}/\mathbb{Z}$ gauge theories. We also briefly discuss relevance for some previously considered physical systems. In particular we comment on a relation to the recently discovered non-invertible symmetry in 4d QED and the problem of categorification of Chern-Simons TQFT.
